The recently emerging field of twistronics provides a variety of examples of quasi-periodic Hamiltonians due to incommensurable twists of two or several lattice structures. While such examples exhibit quasi-periodicity in two spatial dimensions, we shall restrict us here to lattice structures that are periodic in one dimension and quasi-periodic in only one direction that appear naturally by superimposing strained lattices. This has the advantage that the well-developed theory of quasi-periodic one-dimensional discrete operators is applicable. Similarly to the case of magnetic fields, fractal spectra, the so-called Hofstadter butterfly [1]}, [2]}, [3]}, and metal insulator transitions [4]} have been observed in moiré structures, too. The latter by changing the tunneling rate when compressing the lattices. Experimental and theoretical studies of transport properties for one-dimensional moiré structures have been considered in [5]}. We also discuss model operators for analogous results in two spatial dimensions. In contrast to some of their two-dimensional twisted moiré superstructures, one-dimensional models do not exhibit flat bands, see e.g. our Proposition REF .
